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arXiv · 1508.03397

On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map

Maarten de Hoop·Paul Kepley·Lauri Oksanen
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Abstract

We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that the travel time distances for all interior points determine the Riemannian manifold in a stable manner. We do not assume that there are sources or receivers in the interior, and use the hyperbolic Neumann-to-Dirichlet map, or its restriction, as our data. Our algorithm is a variant of the Boundary Control method, and to our knowledge, this is the first numerical implementation of the method in a geometric setting.

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Maarten de Hoop, Paul Kepley, Lauri Oksanen. 2015-08-14. On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map. https://doi.org/10.1137/15m1033010

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